Features and Benefits
- Reflects how students use a textbook; they generally start with the exercises and flip back to the narrative for help if they need it
- Comprehensive exercise sets provide for a variety of student needs and are consistently structured and labeled to facilitate the creation of homework assignments.
- Review Questions check that students have a general conceptual understanding of the essential ideas from the section
- Basic Skills exercises are linked to examples in the section so students get off to a good start with homework
- Further Explorations exercises extend students’ abilities beyond the basics
- Applications present practical and novel applications and models that use the ideas presented in the section
- Additional Exercises challenge students to stretch their understanding by working through abstract exercises and proofs
- Technology Exercises provide additional opportunities for students to use graphing calculators to solve problems.
- AP Practice Questions at the ends of chapters have been updated to reflect the revised content and format of the AP Calculus Exams.
- The AP Calculus Pacing Guide and Guide to AP Calculus have been fully updated to meet the new Curriculum Framework.
- The addition of the Mathematical Practices for AP Calculus (MPACs) to the course description for AP Calculus AB and BC is arguably the biggest change in the new course curriculum from College Board. To help teachers address this important addition, we have included a Guide to the Mathematical Practices for AP Calculus in this text.
- NEW! The new AP® EXAM INSIGHTS feature appears within the AP Practice Questions at the end of each chapter.
Strengths in the narrative include:
- Conversational writing style that reflects the voice of the instructor.
- Plentiful examples, each stepped-out in detail. Within examples, the steps are annotated in blue type to help students understand what took place in each step.
- Figures that are designed to teach rather than simply supplement the narrative. The figures are annotated to lead students through the key ideas, and rendered using the latest software for unmatched clarity and precision.
- Quick Check exercises that punctuate the narrative at key points to test understanding of basic ideas and encourage students to read with pencil in hand.
Organization and presentation promotes learning key concepts, skills, and applications:
- Topics are introduced through concrete examples, geometric arguments, applications, and analogies rather than through abstract arguments. The authors appeal to students’ intuition and geometric instincts to make calculus natural and believable.
- The 400+ Interactive Figures in the eText provide a resource for instructors to help students visualize concepts where chalk or a marker falls short. The exercises that accompany the figures provide an opportunity for students to manipulate them as part of homework.
- Sequences and Series, the most challenging content in BC calculus, has been spread over two chapters to help clarify and pace it more effectively.
- Chapter 8, Sequences and Infinite Series, begins by providing a big picture with concrete examples of the difference between a sequence and a series followed by studying the properties and limits of sequences in addition to studying special infinite series and convergence tests. This chapter lays the groundwork for analyzing the absolute convergence for power series.
- Chapter 9, Power Series, begins with approximating with polynomials. Power series are introduced as a new way to define functions, building on one series by generating new series using composition, differentiation and integration. Taylor series are then covered and the motivation that precedes the section should make the topic more accessible.
The Teacher’s Resource Guide provides a wealth of instructional resources, including:
- Guided Projects – 59 in all – vividly demonstrate the breadth of calculus and provide excursions that go beyond the typical classroom experience. The “guided” nature of the projects provides scaffolding to help students tackle these more involved problems.
- Annotated Table of Contents provides insight into the overall content and organization of the text.
- Learning Objectives and Index of Applications help teachers gear the text to their course goals and students’ interests.